We present a study of the magnetic susceptibility of La_2-xSr_xCoO_4 single
crystals in a doping range 0.3<=x<=0.8. Our data shows a pronounced magnetic
anisotropy for all compounds. This anisotropy is in agreement with a low-spin
ground state (S=0) of Co^3+ for x>=0.4 and a high-spin ground state (S=3/2) of
Co^2+. We compare our data with a crystal-field model calculation assuming
local moments and find a good description of the magnetic behavior for x>=0.5.
This includes the pronounced kinks observed in the inverse magnetic
susceptibility, which result from the anisotropy and low-energy excited states
of Co^2+ and are not related to magnetic ordering or temperature-dependent
spin-state transitions